Given n random variables x1,...,xn (one-dimensional). The following is known (corr() = Pearson correlation):
corr(x1,x2) = a corr(x2,x3) = a
The actual values of the random variables are unkown though. Only some of their correlations are known.
From this, is it possible to calculate
corr(x3,x1) = ?
Or more generally, if the set of correlations
corr(x_i, x_i+1) with
i=[1..c], c<(n-1) are known, is it possible to estimate or directly calculate